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Answer:
Step-by-step explanation:
Given the expression:
x³(x−y)⁷−y³(x−y)⁷
This can also be written as (x³-y³)(x-y)⁷
(x³-y³)(x-y)⁷= (x-y)⁷ (x³-y³)
Expand (x³-y³)
x³-y³ = (x-y)(x²+xy+y²)
Substitute back into the original expression:
(x-y)⁷ (x³-y³) = (x-y)⁷(x-y)(x²+xy+y²)
(x-y)⁷ (x³-y³) = (x-y)⁸(x²+xy+y²)
(x-y)⁷ (x³-y³) = (x-y)⁸(x²+y²+xy)
Comparing the result with (x−y)^m(x^2+y^2+nxy).
(x-y)⁸ = (x-y)^m
m = 8
Also:
nxy = xy
n = xy/xy
n = 1
Hence the value of m is 8
The value of m is 8
The expression is given as:
[tex]x^3(x-y)^7-y^3(x-y)^7[/tex]
Factor out (x - y)^7 in the above expression
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x^3 - y^3)(x -y)^7[/tex]
Expand out (x^3 - y^3) as the difference of two cubes
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x-y)(x\²+xy+y\²)(x -y)^7[/tex]
Combine the common factors
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x\²+xy+y\²)(x -y)^8[/tex]
Rewrite the expression as:
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x -y)^8(x\²+xy+y\²)[/tex]
The expression format is given as:
[tex](x-y)^m(x^2+y2^+nxy)[/tex]
So, we have:
[tex](x-y)^m(x^2+y2^+nxy) = (x -y)^8(x\²+xy+y\²)[/tex]
By comparison, we have:
[tex]m = 8[/tex]
Hence, the value of m is 8
Read more about expressions at:
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